Nanomechanical photonic devices

ABSTRACT

Devices which operate on gradient optical forces, in particular, nanoscale mechanical devices which are actuable by gradient optical forces. Such a device comprises a waveguide and a dielectric body, with at least a portion of the waveguide separated from the dielectric body at a distance which permits evanescent coupling of an optical mode within the waveguide to the dielectric body. This results in an optical force which acts on the waveguide and which can be exploited in a variety of devices on a nano scale, including all-optical switches, photonic transistors, tuneable couplers, optical attenuators and tuneable phase shifters.

This application claims priority from U.S. Provisional Application Nos.61/043,607 and 61/117,792, the contents of which are hereby incorporatedby reference in their entirety.

FIELD OF THE INVENTION

The present invention relates to devices which operate on gradientoptical forces, and to methods of manufacturing such devices; inparticular, nanoscale mechanical devices which are actuable by gradientoptical forces.

BACKGROUND OF THE INVENTION

The optical force is one of the most fundamental properties carried bylight. This force is generally considered too small for macroscopicpractical use. Yet in the microscopic world, optical tweezers have beenwidely used to manipulate atoms and micron-sized dielectric particles infree space.

One natural step forward would be exploiting this principle as a drivingforce in solid state devices such as electromechanical systems. Indeed,recent experiments have elucidated the radiation force of light in highfinesse optical microcavities (see references 1 to 3). However, thelarge footprints involved in these optical microcavities fundamentallylimit the scaling of devices down to nanoscale dimensions where excitingquantum phenomena such as macroscopic quantum coherence, generation ofsqueezed states and optical entanglement start to manifest.

Harnessing optical forces on chip would bring transformational advancesin electromechanical systems by offering efficient and ultrahighbandwidth optical coupling to the sub-micron scale devices. This newtransduction is fundamentally distinctive from conventional charge basedschemes predominately employed in today's solid state devices. Theforces of light stem from two major mechanisms, namely radiationpressure and transverse gradient force.

Radiation pressure induced forces have been extensively studied in thehigh finesse optical cavities, where light field is confined inside thecavity and the moment of light is transferred to the mirror forming thecavity and applies a perpendicular force to the mirror. Analogously,radiation pressure is also detected in the high finesse microspheres ordisk resonators⁶. The transverse gradient force, on the other hand,results from the lateral gradient of propagating light field andtherefore applies a transverse force to a dielectric body. Recently itwas theoretically predicted that this seemingly small force could besignificant in photonic structures due to enhanced light density insubmicron scale photonic waveguides (see reference 4).

Recent theories predicted that the optical force can be enhanced in aphotonic waveguide without the aid of a cavity and can be directly usedfor electromechanical actuation; however, on-chip detection of the forcehas been a significant challenge, primarily owing to the lack ofefficient nanoscale mechanical transducers in the photonics domain.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention, there is providedan optomechanical device comprising a waveguide and a dielectric body,wherein at least a portion of the waveguide is separated from thedielectric body at a distance which permits evanescent coupling of theoptical mode to the dielectric body whereby a transverse gradient forceinduced by the optical mode causes a displacement of the waveguide.

The evanescent coupling of the optical mode to the dielectric bodyresults in an optical force due to the transverse gradient force inducedby the optical mode. This force is found to be substantial in drivingnanomechanical devices.

Preferably, the waveguide is single mode, or configured for single modeoperation.

Optionally, the waveguide comprises a gap defining a first and a secondcantilever portion of the waveguide.

Cantilevering the waveguide means that a greater range of displacementand hence a greater tuning or attenuation range can be achieved.

Preferably, the device further comprises one or both of an input couplerto couple an optical mode into the waveguide and an output coupler tocouple an optical mode out of the waveguide.

Optionally, one or both of the input and output couplers comprise aphotonic crystal adapted to support a single transverse mode.

Optionally, the dielectric body comprises a substrate, a secondwaveguide or a side dielectric body such as a silicon side gate.

Optionally, one of the first or second cantilever portions issubstantially longer than the other of said first or second cantileverportions.

Having one cantilever arm longer than the other means that one canremain relatively stationary and the other can benefit from an increasedrange of movement thus resulting in further improved tuning orattenuation ranges.

Preferably, the input coupler and the output coupler mechanicallysupport the waveguide.

In this way, the couplers which are normally employed only to couplelight into a waveguide may serve a dual purpose thus doing away with theneed for additional components which might introduce additional opticallosses or mechanical problems.

According to a second aspect of the present invention, there is provideda system for high resolution detection of displacement and/or opticalforces, the system comprising a device according to the first aspect,and a first and second laser coupled to the device and employed in apump-probe configuration, wherein the first laser is amplitude modulatedto produce a corresponding modulation of the optical force on thewaveguide and the second laser provides a probe signal to allowinterferometric detection of the effects on the waveguide produced bythe modulation.

According to a third aspect of the present invention, there is provideda photonic transistor comprising a gate waveguide which receives anoptical signal, a device according to the first aspect, and an opticalresonator positioned there between, wherein the optical resonator iscoupled to the gate waveguide and to the device waveguide such thatmodulation of the optical signal produces a corresponding modulation ofthe optical force on the device waveguide.

Preferably, the photonic transistor further comprises a first lasercoupled to the device, whereby modulation of the optical signal withinthe gate waveguide produces a modulated output at the device outputcoupler.

According to a fourth aspect of the present invention, there is provideda photonic switch comprising a device having a cantilevered waveguideaccording to the first aspect, a control bus, and an optical resonatorpositioned therebetween, wherein the optical resonator is coupled to thecontrol bus and to the device waveguide such that the optical resonatordisplaces at least one of the first and second cantilever portions ofthe device waveguide responsive to an optical signal in the control bus.

According to a fifth aspect of the present invention, there is provideda measurement device comprising a device having a cantilevered waveguideaccording to the first aspect, wherein a measurement signal is collectedby coupling to the device substrate.

Optionally, a measurement signal is obtained by measuring the reflectionof the optical mode within the device waveguide at the gap.

According to a sixth aspect of the present invention there is provided atuneable coupler comprising a device according to the first aspect, thedevice comprising a second waveguide spaced from and substantiallyparallel to the first waveguide, said first waveguide and secondwaveguide optically side-coupled such that the optical force produced bythe optical mode causes a relative movement of one waveguide relative tothe other so as to modify the coupling intensity therebetween.

According to a seventh aspect of the present invention there is provideda tuneable phase shifter comprising a device according to the firstaspect, wherein an optical force is applied to deflect the devicewaveguide so as to produce a phase change affecting the optical mode.

According to an eighth aspect of the present invention synchronisedoscillator comprising a device according to the first aspect, the devicecomprising a second waveguide in series with the first device waveguide.

Preferably, the device comprises three or more waveguides arranged insaid series relationship by connecting the output of each device to theinput subsequent device, the output of the last such waveguide resonatorcoupled to the input of the first such resonator.

BRIEF DESCRIPTION OF THE FIGURES

The present invention will now be described by way of example only andwith reference to the accompanying figures in which:

FIG. 1 illustrates the substrate coupled waveguide gradient force. 1 ais a three dimensional schematic illustration of a free-standingwaveguide beam 1 supported by two multimode interference structures 2,with an overlay of the optical mode plot. 1 b illustrates the result offinite element simulation showing the E_(x) component of the opticalfields in the waveguide 1 evanescently coupled to the dielectricsubstrate 3 at the separation gap g, with the black curve on the rightshowing the magnitude of E_(x) at the cross-section through the centreof the waveguide 1. E_(x) is continuous at the bottom surface of thewaveguide 1 and at the top surface of the substrate 3. 1 c and 1 d showthat the effective refractive index of the waveguide (1 c) and theoptical force on the waveguide (1 d) strongly depend on the separationg.

FIG. 2 illustrates, in schematic form, an experimental set-up and devicesystem. 2 a shows the measurement set-up. 2 b is a scanning electronmicrograph of a free-standing, 10 micron long NEMS beam 1. 2 c shows thefinite-difference time-domain simulation of the mode conversion from theMMI coupler 2 into the NEMS beam. 2 d shows the finite elementsimulation of the mechanical mode shape of the waveguide beam 1, withthe strain distribution displayed in shading.

FIG. 3 illustrates the device characterisation and experimentaldemonstration of the waveguide gradient force. 3 a shows the typicaltransmission spectrum of a device, showing the fringing caused by theFabry-Perot etalon formed by the input and output couplers. The markerat the peak is the actuation wavelength and the marker two fringes tothe right is the probe wavelength. 3 b shows the resonance curves of a10 micron long waveguide beam at varying modulation levels of theactuation light. When the vibration amplitude exceeds the criticalamplitude, the response shows a strong softening nonlinearity. Thecritical amplitude of 2.5±0.1 nm, determined from the backbone curve,agrees well with a theoretical value of 2.2. Inset, the vibrationamplitude versus modulated optical power on the device shows a linearresponse. 3 c and 3 d show the measured noise showing Lorentzianthermomechanical peaks of beams 10 and 13 microns long (respectively).In 3 e, the optical force is measured on devices with various beamlengths and substrate separation sizes.

FIG. 4 illustrates the measurement of the thermal response of thedevice. 4 a is an optical micrograph of the Mach-Zender interferometer(MZI) device 10. The path length is 100 microns longer at the top arm 11than the bottom arm 12. In 3 b, the transmission spectrum of theMach-Zender device shows the interference fringes expected, with goodvisibility even after release of the waveguide. The right markerindicates the actuation and the left marker the detection lasers. Theinset shows an extinction ratio of ˜30 dB in the range presented. 4 c isa wide frequency measurement of the effective index response of the MZIdevice with (upper trace) and without (lower trace) the released NEMSbeam. The lower trace has a −log(f) dependence on frequency due to thethermo-optical nonlinear effect. The distinct response shown by theupper trace at low frequency is due to the slow thermal response of thesuspended beam. 4 d shows the dynamic temperature variation of thereleased NEMS beam versus frequency as well as of the unreleasedwaveguide. 4 e shows the measured mechanical resonance response of thebeam. The contribution from the optical force is three orders ofmagnitude higher than that from the thermal force.

FIG. 5 illustrates the tuning of nanomechanical resonance by (5 a)varying the static or “dc” component of the actuation light power and by(5 b) raising the temperature of the substrate. If thermal effectsdominated in the device, adding static optical power would have asimilar effect on the mechanical properties as raising the temperature.The opposite is shown in 5 a and 5 b which rule out the possibility thatit is in fact photothermal force and not the optical force that isactuating the device.

FIG. 6 illustrates the ultrasensitive measurement of thethermomechanical motion of nanocantilevers. 6 a demonstrates themeasurement set-up, 6 b shows the measured noise power spectral densityof the optical detection signal showing the room-temperaturethermomechanical resonance peaks of both cantilevers and 6 c shows thecorresponding displacement PSD of the second nanocantilever, showing adisplacement measurement noise floor of 40 fm/Hz^(1/2).

FIG. 7 illustrates optical actuation of the nanocantilevers. 7 a showsthe driven response of the waveguide nanocantilevers. Thenanocantilevers are actuated by the gradient optical force generated bythe amplitude modulated laser. The phase shows a clear 180° change ateach resonance. 7 b shows the resonance amplitude of the firstcantilever at increasing actuation optical power, as marked in theinset. The optical force is determined to be 0.5±0.1 pN/μm/mW from thecalibrated resonance amplitude and optical power.

FIG. 8 shows in schematic form a first example of a practical deviceembodying one or more aspects of the invention which takes the form of aphotonic transistor 20.

FIG. 9 a shows in schematic form a photonic switch 30 embodying theinvention, and 9 b shows a practical application of the photonic switchbeing employed to cut off an optical sub-circuit which is known to bebad.

FIG. 10 illustrates end-to-end cantilevered waveguide nanolevers 41,42embodying one or more aspects of the invention.

FIG. 11 illustrates a light force tuneable photonic coupler 50 embodyingone or more aspects of the invention.

FIG. 12 illustrates a tuneable phase shifter 60 which operates byoptical force which embodies one or more aspects of the invention.

FIG. 13 illustrates in schematic form a tuneable filter 70 whichembodies a number of aspects of the invention, namely a cantileveredwaveguide 71, a tuneable coupler 72 and a tuneable phase shifter 73.

FIG. 14 illustrates a photonic bus synchronised oscillator 80 thatembodies one or more aspects of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The Applicant is the first to demonstrate the gradient optical forcewhich beforehand had only been theoretically predicted. Furthermore, theApplicant has demonstrated the practical application of the gradientoptical force in a silicon photonic circuit, and further establishedthat this force can be substantial in driving micro- and nanomechanicaldevices.

Detection of optical forces in an integrated silicon photonic circuithas been made possible through an embedded nanomechanical resonator. Thedisplacement caused by the optical force is detected through evanescentcoupling of the nanomechanical resonator to a dielectric substrate. TheApplicant has made the surprising discovery that at modest optical powerthe optical force produced in this way on a photonic waveguide issignificant, with a magnitude comparable to that of most commonly usedactuation forces in electromechanical systems.

The gradient optical force is distinct from radiation pressure which isthe result of the transfer of momentum from photons to mechanicalstructures on which they impinge. The transverse gradient force howeveroriginates from the lateral gradient of a propagating light field.Gradient force is generated by asymmetrically engineering the confinedlightwave mode in an optical waveguide. It only becomes significant whenthe cross section of the waveguide is comparable to the wavelength ofthe guided mode. Due to the strong confinement of light in a submicronwaveguide, the optical force is significantly enhanced at smallerdimensions.

Controlling and harnessing the gradient optical force as taught hereinallows solid state devices to operate under new physical principles.Immediate applications include all-optical switching, reconfigurablephotonics etc. The following examples illustrate a generic configurationto exhibit the optical force effect which forms the basis for variousdevices subsequently described, and nanoscale mechanical structures areintroduced which, for example, may have masses on the order of picogramsand which are significantly affected by tiny optical forces.

The configuration is schematically shown in FIG. 1. Instead oftwo-coupled waveguides (as described in references 3 and 4), here onlyone free-standing single mode waveguide 1 is utilized. The force on thesingle waveguide 1 can be understood similarly to the coupled waveguidepair in which the eigen-energy of the system is dependent on the gapbetween the waveguide and the substrate. An alternative formalism toderive the force is to consider the asymmetric distribution of theMaxwell stress tensor along the cross-section of the waveguide with theproximity of the substrate. Then the force on the waveguide can beevaluated directly by integration of Maxwell stress tensor on thewaveguide surface. The analytical and numerical calculation methods aresimilar to those disclosed in reference 3.

FIG. 1 a is a three-dimensional schematic illustration of afree-standing waveguide beam 1 supported by a multimode interferencestructure 2 at each end. The overlaid optical mode plot displays thein-plane electrical field distribution of TE mode E_(x), calculated byfinite-element-method (FEM) simulation. The asymmetric guided mode inthe free standing waveguide is weakly evanescently coupled with thesubstrate 3, and it is the corresponding field gradient that produces anet optical force on the waveguide 1.

At a given optical input power, this force on the waveguide 1 stronglydepends on the gap between waveguide 1 and substrate 3 as plotted inFIG. 1 d. The results clearly show that the magnitude of the opticalforce is on the order of piconewton per micrometer, which is substantialfor actuating nanomechanical devices. As the gap is varied, theeffective refractive index n_(eff) of the waveguide system is rapidlymodulated, as shown in FIG. 1 c. Thus the transverse displacement of thewaveguide 1 will induce a phase shift in the device which is measured byon-chip phase-sensitive interferometers. This phase shift can beexpressed as:

$\begin{matrix}\begin{matrix}{{\delta\varphi} = {\delta \left( {\frac{2\pi}{\lambda}n_{eff}l} \right)}} \\{{= {\frac{2\pi}{\lambda}\left( {{l\frac{\partial n_{eff}}{\partial z}} + {n_{eff}\frac{\partial l}{\partial z}}} \right)\delta \; z}},}\end{matrix} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where λ is wavelength and l is the length of the nanomechanical beam andδz is the beam displacement. The first term is dominant while the secondterm is negligible. Through the measuring the motion of thenanomechanical beam, the optical force can be quantified with highsensitivity.

The force generation scheme discussed here is very universal, and manydifferent device variations might be derived from the Applicant'sgeneric device design. Such an integrated silicon photonic circuit isessentially CMOS compatible.

To demonstrate this optical force, the Applicant exploits the highsensitivity offered by nanoelectromechanical systems (NEMS) integratedin a silicon photonic circuit fabricated with a CMOS compatible process.An example of such a circuit is shown in FIG. 2. The simplest formconsists of a single mode strip waveguide 1 enclosed by two gratingcouplers 2 (FIG. 2 b). To form the air bridge waveguide 1, a portion ofthe waveguide 1 is released from the substrate 3 by chemically removingthe silicon dioxide layer underneath. This released part of thewaveguide 1 becomes an embedded NEMS beam in the photonic circuit. Ascanning electron microscope picture of an exemplary suspended, 10 μmlong, 500 nm wide beam is shown in FIG. 2 b. The separation gap betweenthe beam 1 and the substrate 3 can be varied during fabrication bycontrolling the etching time, and typically achieved in the range of300-600 nm.

The use of grating couplers 2 enables efficient coupling of light intoand out of the planar waveguides with an out-of-plane optical fibrearray. The Applicant has routinely achieved coupling efficiency of 14%(or −8.5 dB) during the fabrication process.

To provide better mechanical clamping and obtain reproducible deviceswith varying lengths, two low-loss multimode interference (MMI) devices2 are fabricated to define and support the suspended waveguide beam 1 asshown in FIG. 2 c. The MMI design is optimized to provide low opticalinsertion loss meanwhile maintain high mechanical quality factor. Thepair of MMI couplers 2 in the illustrated example introduces additional6 dB optical loss.

Nanomechanical devices are known to be superior force sensors (seereference 7). The force applied on the beam 1 induces the device'snanomechanical motion, which is further amplified if the force ismodulated at the device's mechanical resonance frequency. In thedescribed photonic circuit configuration, the suspended beam 1,including the air gap, comprises a part of the waveguide. The phase ofthe propagating light is modulated by the transverse motion of the beam1, which changes the air gap size and thus alternates the effectiveindex of the waveguide mode (as illustrated by FIG. 1 c). Using anon-chip interferometer, such as a Fabry-Perot or Mach-Zehnderinterferometer, this phase change can be read out as transmissionamplitude variation through the device.

In the measurement setup illustrated in FIG. 2 a, two wavelengthtuneable laser sources 5,6 are used in a pump-probe scheme; one of which(6) is amplitude modulated to generate a dynamic (i.e. time-varying)optical force on the beam 1 and the other (5) acts as the probe for thedisplacement readout. The TE mode is selected by the polarizationcontroller 7 and launched into the device through one single-modepolarization-maintaining (PM) fibre aligned with the input coupler.

Another fibre aligned with the output coupler collects the transmittedsignal. The overall transmission of system is near 4×10⁻³ (or −24 dB)with most loss at the grating couplers (−10±1 dB each) and the two MMIcouplers 2 (−4 dB total). In FIG. 3 a, the transmission spectrum of atypical device is shown. The grating coupler shows a bandwidth of nearly20 nm. The transmission oscillates with the wavelength at a periodicityof ˜1.9 nm, corresponding to the free spectral range (FSR) of theFabry-Perot interferometer formed between the two grating couplers. Thefringes allow interferometric detection of the motion of the device,with the wavelength of the actuation laser is set at the maximum slopeof the transmission. The probe laser wavelength is offset by 5˜10 nmfrom the actuation wavelength to allow sufficient filtering of actuationlight before the photodetector.

The sensitivity of the system is first calibrated, by measuring thedevice's thermomechanical motion. The displacement noise power spectraldensity (PSD) of the beam at its resonance can be expressed as S_(z)^(1/2)=√{square root over (4k_(b)TQ/(mω₀ ³))}, where k_(b) isBoltzmann's constant, T is the absolute temperature, Q is the mechanicalquality factor, ω₀ is the angular resonance frequency and m is theeffective mass. For a 10 μm long beam with a resonance frequency of 8.87MHz and quality factor of 1,850 in vacuum, S_(z) ^(1/2) is calculated tobe 3.8×10⁻¹³ m·Hz^(−1/2). This thermomechanical motion induces phasenoise in the interferometer and thus the transmitted intensity of theprobe light. FIG. 3 c shows the measured output noise spectrum at thephotodetector with 12.5 mW probe light power. Using calculateddisplacement noise value, the noise floor of the spectrum corresponds todisplacement noise PSD of 7.2×10⁻¹⁴ m·Hz^(−1/2). The total 5pW·Hz^(−1/2) optical power noise floor is comprised of detector noise(2.5 pW·Hz^(−1/2)) and the noise from the diode laser and laseramplifier (noise figure ˜5 dB).

To measure the dynamic response of the device, a network analyzer 8 isused to modulate the actuation laser's amplitude and measure thefrequency dependence of the transmitted probe signal. In FIG. 3 b, theoptically driven mechanical response of the devices at varying pumplight modulation amplitude is shown. The measured mechanical resonanceof the waveguide beam shows a quality factor of ˜2000. The actualoptical power on the waveguide beam can be derived from the transmittedpower, taking account of the intra-cavity enhancement factor of theFabry-Perot interferometer (see reference 8). The corresponding drivingforce on the beam can be calculated from the beam's vibration amplitude.In this way, the optical force magnitude can be determined at any givenoptical power. For the beam with a separation of 360 nm from thesubstrate, the optical force is evaluated to be 0.45 pN/μm/mW. Thisvalue agrees well with the theoretical results presented in FIG. 1 d andin the literature.

When excited to high vibration amplitude, the waveguide beam 1 behavesnonlinearly, displaying an uncommon frequency-softening effect due tothe residual compressive stress in the silicon film. The criticalamplitude of the nonlinearity is given by a_(c)=ω₀(L/π)²(√{square rootover (3)}ρ/EQ)^(1/2) theoretically and can be determined by fitting thebackbone curve which connects the maxima of the resonance responsecurves. From the data shown in FIG. 3 b, the critical amplitude ismeasured to be 2.5 nm, fairly close to the theoretically determinedvalue of 2.14 nm. This provides yet another calibration of the opticalforce measurement.

As illustrated in FIG. 1 d, the optical force is a function of theseparation gap g between the waveguide beam 1 and the substrate 3. Tofurther elucidate the mechanism of the optical force, the Applicant hasmeasured several devices with varying gap sizes as well as the beamlengths; the result of which is shown in FIG. 3 e. The measured opticalforce shows clear dependence on the gap size, indicating good agreementwith the theoretical model. It is also found the optical force is notdependent on the length of the beam. This rules out the photothermaleffect as the mechanism of the observed optical force which should beindependent of g but increases with beam length due to thermal heatingand expansion from optical absorption.

The optical force can also be quantified by static force measurement. Astatic “dc” optical power on the beam will also exert a static force onit. This static optical force is observed experimentally by measuringthe resonance frequency shift of the beam due to increased probe lightpower. During such measurement, the actuation light power and modulationamplitude are kept constant, and the probe light power is tuned. It isclear from the exemplary data presented in FIG. 5 a that the resonancefrequency shifts upwards with increasing optical power. Again, thisrules out the photothermal effect as the cause for the resonancefrequency is observed to have a negative temperature coefficient in acareful temperature controlled experiment, as illustrated in FIG. 5 b.The positive frequency shift can be explained by the increased tensionin the beam by the increasing static optical force as more optical poweris added. The measurement results show the resonance frequency is tunedby optical power at 7.5 kHz/mW. This frequency shift is intensified bythe curvature of the beam due to the buckling caused by the residualstress from the fabrication. A simple finite element modelling producesvery accurate estimation of this frequency tuning effect. The fitting tothe frequency shift yields a static optical force of 0.5 pN/μm/mW, ingood agreement with dynamic force measurement.

The magnitude of this transverse optical force on the waveguide iscomparable with other types of charge-based actuation forces commonlyemployed in nanomechanical devices, such as capacitive, piezoelectricand magnetic forces. Further, at nanoscale, electromechanical motionsignals are exceedingly small. These tiny signals are generallydominated by parasitic signals on the chip, mostly from direct couplingfrom the electrical actuation signal. In the photonic waveguide, thereis minimum cross-talk between photons in the actuation channel and thesensing channels. The all-optical scheme presented herein not onlyprovides efficient actuation, but also significantly improves the signalquality of a nanomechanical resonator.

Even more significantly, the force generated in optical frequency domainpromises an enormous operation bandwidth. This bandwidth isfundamentally limited by the carrier light frequency (2×10¹⁴ Hz).Practically this is limited by the bandwidth of the input-outputcouplers (2.5 THz) implying 3 orders of magnitude improvement over whathas been obtained with known electronic actuators. This extremely widebandwidth (<ps response time), in combination with the high transductiongain, low readout noise will allow a broad range of exciting experimentsand devices based upon ultrafast detection and sub-picosecondstroboscopic measurement.

Beyond, arrays of spatially separated nanomechanical resonators can befabricated along a photonic “bus” for efficient synchronization and highspeed optical intercommunications. In this way, one can achievelong-range coherent signal processing without locally addressingindividual devices. This eventually will lead to large scale integrationof nanomechanical structures and enable new device functions in bothmechanical and optical domains.

The strong coupling of light and mechanical oscillation will produce ahost of interesting new phenomena that finds practical use as describedfurther herein and in a host of other envisaged applications, such asmechanical Kerr effect, optomechanical parametric amplifications,all-optically controlled tuneable filters, couplers, (de)modulators,mixers etc. On the fundamental fronts, recently we have evidenced hugestride in advancing micro and nanomechanical systems to approachingquantum regimes.

The techniques presented herein seamlessly integrate nanomechanicaldevices that are size-matched to photonic waveguides meanwhile offershighest engineering flexibility. The elucidated optical force allowsefficient coupling between optical field and mechanical vibration at thesmallest obtainable mechanical and optical volumes, simultaneouslyproviding high bandwidth and the sensitivity that is required forcoherent control of nanomechanical structures. It is foreseeable thatultra-high frequency, active cooled or self cooled, practical quantumdevices could become a realistic prospect through exploitation of thetransverse optical forces as presented herein.

The devices disclosed herein were fabricated on a silicon-on-insulator(SOI) wafer. The silicon layer is thinned down by thermal oxidation andsubsequent wet etch. The devices (waveguides and couplers) were thenpatterned by electron beam lithography and a plasma dry etching process.

The cantilevers are then released from the substrate using aphoto-lithography patterned mask and buffered oxide etching (BOE).

In addition to achieving all-photonic transduction of the nanomechanicalbeam, it is possible to detect the displacement of the beam withouthaving to employ interferometric techniques.

An exemplary cantilevered waveguide 40 is illustrated in FIG. 10. Thewaveguide is similar to the waveguide described above, however duringfabrication a gap 43 is created such that the suspended waveguide iscantilevered.

Movement of the cantilever modulates the total transmission of thecircuit and as such the displacement is measured in the transmittedoptical signal. The Applicant has demonstrated displacement sensitivityof 40 fm/Hz^(1/2) at room temperature, which is comparable withstate-of-the-art milli-kelvin detection techniques of similarnanomechanical devices.

In the illustrated waveguide the cantilevers 41,42 are 3 μm long with alateral gap 43 between them of 200 nm. The estimated optical loss causedby this relatively small (compared to the optical wavelength) is ˜3 dB.FIG. 10 c presents the simulated transmission from one cantilever to theother as a function of the vertical offset of the left cantilever. Theasymmetry in the transmission profile is due to the additional couplingof the optical fields in the waveguide to the substrate.

An exemplary measurement setup is illustrated in FIG. 6 a. An array offibres is aligned to the grating couplers to provide convenient inputand output of optical signals. Light from two tuneable diode lasers 5,6at different wavelengths is coupled into the device which is mounted ina vacuum chamber with a base pressure of 1×10⁻⁵ Torr. The first laser 6is amplitude modulated to apply an optical actuation force to thedevice. The second detection laser 5 is used in CW mode and itstransmission through the circuit is measured with a photodetector. Anarrow band etalon filter 9 removes the light at the actuationwavelength before reaching the photodetector in order to optimize themeasurement dynamic range. The frequency response and noise spectrum ofthe photodetector signal is then measured with a network/spectrumanalyzer 8.

The sensitivity of the system is first assessed by measuring thethermomechanical motion of the devices when the actuation laser isturned off. In FIG. 6 b, the noise power spectrum density (PSD) of thetransmitted detection laser signal in a wide frequency range isdisplayed. The applied optical power at the input coupler is 50 mW; thecalibrated power on the first cantilever is −7.5 mW; after propagatingthrough the circuit 200 pW power is received at the photodetector.

The spectrum shows two prominent peaks at 13.07 and 13.36 MHz,corresponding to the out-of-plane fundamental mechanical resonances ofthe two cantilevers. The difference of their resonance frequency is dueto the slight misalignment of the etching window during the wet etching,causing a different undercut at the clamping point. The two resonancesshow nearly identical quality factors of −4500 in vacuum. The spectraldensity of thermomechanical displacement noise at the resonancefrequency is S_(z) ^(1/2)=√{square root over (4k_(B)T₀Q/(mω₀ ³))} wherek_(B) is the Boltzmann constant, T₀ is the absolute temperature (300K),Q is the mechanical quality factor, ω₀ is the angular resonancefrequency and m the modal mass of the cantilever. The twothermomechanical resonances have different values due to their differentresonant frequencies.

By comparing the expected displacement noise with the measured noisespectrum, we can determine the displacement sensitivity R₀=δT/δz of thesystem, which is found to be 1.6 μm⁻¹, close to the numerical predictionat ˜25 nm offset (FIG. 8 d). In FIG. 6 d, the noise floor of themeasured noise spectrum is 16 pW/Hz^(1/2), translates to 40 fm/Hz^(1/2)displacement resolution at 7.5 mW optical power on the left cantilever.The noise level is constituted by the 13 pW/Hz^(1/2) noise equivalentpower (NEP) of the photodetector and the 9 pW/Hz^(1/2) shot-noise of the200 μW optical signal. The achieved displacement sensitivity isremarkable considering the simple room temperature measurementconfiguration. By improving the grating couplers and using a higherpower laser source, the detection sensitivity can reach the shot-noiselimit and be further improved as P^(−1/2).

When the actuation laser 6 is turned on and its amplitude is modulated,an oscillating gradient optical force is applied to the waveguidecantilevers 41,42. Photothermal excitation can be neglected because itis found to be three orders of magnitude weaker than the gradientoptical force. The temperature rise from photothermal absorption isestimated to be on millikelvin level, due to the low absorptioncoefficient at telecomm wavelength and the high thermal conductivity ofsilicon. The driven response of the devices in amplitude and phase isshown in FIG. 7. The two cantilevers 41,42 show different resonantamplitudes. This is expected because the actuation optical powers on thetwo cantilevers are different due to the loss (˜3 dB) occurring at thegap between them. Thus we can attribute the resonance peak at 13.07 MHzto the cantilever on the left, whose amplitude is around twice that ofthe one at 13.87 MHz since the light is launched into the devices fromthe left coupler.

Using the calibrated responsivity R₀ of the system, the vibrationamplitude can be determined from the measured signal. At the resonancefrequency, the driving force F is related to the vibration amplitudea(w₀) of the cantilever by F=ka(ω₀)/Q. In FIG. 7 b, the resonantresponse of the first cantilever is measured in dependence of lasermodulation amplitude, showing a linear relationship. The optical forcecan then be derived as ˜0.5±0.1 pN/mW/μm, in close agreement with themeasured value in similar state-of-the-art photonic circuits. Themeasurement error is mostly due to the uncertainty in determining of theactual optical power on the device.

The gradient optical force originates from the asymmetric optical fieldgradient in the waveguide due to coupling with the substrate. Therefore,this force, as well as the optical detection method described above, isintrinsically wideband. Thus, this complete optical transduction schemecan potentially gain unprecedented operation bandwidth. The amplitudemodulation detection that is applied here is essentially anon-interferometric method. It is distinct from interferometric methodsin which the mechanical motion induced optical phases shift is measured.Thus the measurement does not require a coherent light source and isimmune to the phase noise of the laser. For practical sensingapplications, the non-interferometric detection method is especiallyattractive because integrated low-cost light sources can be used. Withfuture development of other integrated photonic components, includinglight sources, modulators and detectors, an entire couplednanomechanical-nanophotonic system can be realized on a single chip.Such a compact, robust system with high sensitivity will find a widerange of applications, such as chemical and biological sensing andoptical signal processing.

The Applicants have been able to create a number of devices that makeuse of the present invention, some of which are now described toillustrate the practical application of the above techniques.

FIG. 8 illustrates in schematic form a first practical embodiment of thepresent invention, taking the form of what might be termed a photonictransistor 20. The photonic transistor comprises a gate waveguide 21which serves as a signal input for a control signal. A high Q opticalresonator 22 is coupled to the gate waveguide 21 so as to enhance theinput optical signal; for the purposes of this example the resonator 22is a microdisk resonator but may be a of a ring or racetrack type.

A second waveguide 23 (shown schematically) is coupled to the opticalresonator and, in accordance with the invention, is suspended (i.e.spaced from the substrate) so as to form a nanomechanical resonator. Theinteraction between the optical resonator 22, which acts as a forceamplifier, and the suspended waveguide 23 (nanomechanical resonator)means that a CW optical signal propagating within the waveguide 23 canbe modulated by an optical signal within the gate waveguide 21. This isanalogous to an electronic transistor whereby the current at the basedetermines whether charge may flow between the emitter and collector.

In the photonic transistor, a high optical Q and a high mechanical Q canresult in the input signal in the gate waveguide 21 being amplified,much in the same way that an electronic transistor is employed in acommon emitter amplifier. In this way, a small input modulation canresult in, effectively, an amplification of this modulation within thesuspended waveguide 23.

FIG. 9 illustrates in schematic form a second practical embodiment ofthe present invention, taking the form of what might be termed aphotonic switch 30. In this embodiment, two cantilevered waveguides31,32 are embedded in a photonic circuit. As described above, thebuckling of one cantilever by an applied optical force modifies thetransmission of that waveguide.

The photonic switch can be used in the opposite sense to prevent anoptical signal being relayed to a part of the optical circuit that isbad by cutting off that part of the circuit.

FIG. 9 b illustrates such a practical example. A signal bus 35 within anoptical circuit has a number of branches, one of which is connected to asub-circuit 36 which is known to be bad. This branch has a cantileveredwaveguide 32 in accordance with the present invention and is operativelycontrolled by a control bus 31 by way of a disk resonator 33 to whichboth are optically coupled. A signal sent to the control bus 31 causes adisplacement of one of the cantilevered portions of the waveguide 32,thus “cutting off” the bad sub-circuit 36.

In addition, because the cantilevered waveguide permits variableattenuation of an optical signal, the photonic switch 30 can also beused to control the amount of optical power within an optical signalthat is passed on to various sub-circuits forming part of a largerphotonic circuit. In FIG. 9 b above, it is clear that a control signalof less power would cause a smaller displacement of the cantileveredportion of the waveguide 32 and attenuate, rather than cut off, theoptical signal.

Note that in such embodiments, it is advantageous that one of thecantilevered portions of the waveguide is substantially elongatecompared to the relatively shorter other cantilevered portion. Havingsuch a longer cantilevered portion means that a greater range ofdisplacement can be achieved; the other cantilevered portion beingshorter means that it is comparatively stationary while the other isfree to move. However, having two cantilevered portions of more or lessequal length may still serve the same purpose although the same degreeof tuning may be harder to achieve.

It is of note that a cantilever has a greater range of movement than acontinuous beam and as such even having cantilevered portions of similarlength can produce a larger attenuation range.

A further application of such a device is as a nanomechanical opticalmodulator, whereby the light passing through the photonic circuit can bemodulated. To effect such modulation, a corresponding modulation wouldbe applied to the control line. In a similar fashion to the photonictransistor shown in FIG. 8 and described above, such modulation could ofcourse be amplified, thus allowing a comparatively smaller controlsignal modulation to effect a larger modulation within the opticalcircuit.

A combination of a number of such photonic switches clearly may be usedto provide a comprehensive array of controls over an optical circuit;determining which sub-circuits receive an optical signal, the power ofthe optical signal that said sub-circuit receives, as well as providingprotection in the form of automatic or selective cut-offs to eitherprotect sub-circuits or isolate non-working sub-circuits.

For metrological applications, a cantilevered waveguide as illustratedin FIG. 10 can be used as a scanning probe 40. FIG. 10 a is an opticalmicroscope image of end to end coupled waveguide nanocantilevers 41,42in the middle of a waveguide and a grating coupler at each end. FIG. 10b is a scanning electron microscope image of the suspended portion,clearly showing the separation 43 in the suspended waveguide thatcreates the two cantilevers 41,42. As described in detail above,relatively minor displacement of the cantilevers results in a dramaticeffect on the transmission of the device.

FIG. 11 illustrates a tuneable coupler 50 in a photonic filter in whichtwo freely suspended waveguides 51,52 extend parallel to, and areoptically side-coupled to, one another. A tuneable coupler is anessential component in a photonic filter and the coupler illustratedhere tunes the gap between the waveguide 51 and the optical resonator53. An all-optical device such as this does away with the need formaterial doping and electrode deposition because unlike state-of-the-arttuneable couplers no thermal heating or electrostatic tuning isrequired.

When an optical force is applied, i.e. by inserting a “tweezer” lightsignal into the second waveguide 52, the suspended waveguides 51,52 movewith respect to each other, thus modifying the gap therebetween. Thechange in the gap causes a corresponding modification of the couplingintensity between the waveguides 51,52 and also between the firstwaveguide 51 and the optical resonator 53.

If the ring resonator is used as a wavelength filter, achieving a highextinction ratio requires close matching between the amplitude loss perround trip and the coupling coefficient. However, precision matching isdifficult to achieve with state-of-the-art microfabrication techniques.The illustrated coupler 50 allows precise control of the gap spacingbetween the waveguide 51 and the microresonator 53 and as such highestextinction can be achieved. FIG. 11 b illustrates the change in the gapcaused by the “tweezer” light signal, and FIG. 11 c demonstrates how inthis example a 30 dB extinction ratio may be achieved within 50 nm oftuning.

Tuneable phase shifting can also be realised in a device 60, asillustrated in FIG. 12, which is fabricated as a portion of a waveguideor embedded in a microresonator to achieve precise phase matching. Themajor advantage of this is the negligible insertion loss that can beachieved.

The phase tuning is achieved by changing the refractive index of thewaveguide 61. An analogy may be drawn between a tuneable capacitorconsisting of two parallel plates in which the gap can be modified. Thevariance of this gap in the optical system is provided by the opticalforce which in turn provides the phase tuning.

The coupling between the waveguide 61 and the dielectric substrate 62from which it is spaced acts like an electromagnetic buffer that storesthen releases energy in the form of light, thus introducing a phaseshift to a propagating optical signal.

When the device 60 is placed in a microresonator, the phase tuningeffect can be significantly enhanced because the circulating power isenhanced by the optical finesse of the microresonator, addingproportionately to the optical force.

Tuneable switches (e.g. 71), phase shifters (e.g. 73), and couplers(e.g. 72) can be further used as building blocks to assemble morecomplex photonic filters (e.g. 70). These filters could be engineered tohave multiple poles and zeros depending on the numbers and thetopologies of these tuneable components. Although there are manyconfigurations one can devise for actual filter implementation, weexemplify a typical filter construction 70 in FIG. 13 which represents atwo-pole two-zero filter. The mechanically-deformable tuneable devices71,72,73 are utilized as active control elements to set the couplingratios and phases of each individual ring resonator 74, which in turndetermine the zeros and the poles of the filter.

A synchronised oscillator 80 is illustrated in FIG. 14. A series of(example shown: four) nanomechanical resonators 81,82,83,84 arefabricated on the same photonic bus 85. The light travelling along thebus passes from one resonator to the next and thus provides asynchronising force on all the nanomechanical resonators.

In addition, the light may be further looped back from the lastresonator 84 to the first resonator 81 which enhances saidsynchronisation. Such synchronised oscillators will be ideal for us asultrastable signal sources because of the very low phase noise that canbe achieved in such a configuration.

Further modifications and improvements may be added without departingfrom the scope of the invention as defined by the appended claims.

REFERENCES

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1. An optomechanical device comprising: a waveguide; a dielectric body; wherein at least a portion of the waveguide is separated from the dielectric body at a distance which permits evanescent coupling of a guided lightwave to the dielectric body; and wherein a transverse gradient force induced by the guided lightwave causes a displacement of the waveguide.
 2. A device as described in claim 1, wherein the waveguide is a single mode waveguide, or configured for single mode operation.
 3. A device as described in claim 1, wherein the waveguide comprises a gap defining a first and a second cantilever portion of the waveguide.
 4. A device as described in claim 1, wherein the dielectric body comprises a substrate, a second waveguide or a side dielectric body such as silicon, silicon nitride or silicon dioxide.
 5. A device as described in claim 1, further comprising one or both of an input coupler to couple an optical mode into the waveguide and an output coupler to couple an optical mode out of the waveguide.
 6. A device as described in claim 5, wherein one or both of the input and output couplers comprise a photonic crystal adapted to support a single transverse mode.
 7. A device as described in claim 3, wherein one of the first or second cantilever portions is substantially longer than the other of said first or second cantilever portions. 8-17. (canceled) 